Boyle’s conjecture and perfect localizations

ABSTRACT

In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle’s conjecture is true for left QI-rings with finite Gabriel dimension such that every hereditary torsion theory in the Gabriel filtration is perfect. As corollary, we get that Boyle’s conjecture is true for left QI-rings which satisfy the restricted left socle condition, a result proved by Faith in [6].

KEYWORDS:

• Hereditary torsion theory
• left hereditary ring
• left QI-ring
• left V-ring
• perfect localization

2010 Mathematics Subject Classification:

• 16D25
• 16D50
• 16D70
• 16D90

Acknowledgments

The authors are very thankful to the referee for her/his comments on this paper which helped to improve it.